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AAR-based decomposition algorithm for non-linear convex optimisation

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  • Nima Rabiei
  • Jose Muñoz

Abstract

In this paper we present a method for decomposing a class of convex non-linear programmes which are frequently encountered in engineering plastic analysis. These problems have second-order conic memberships constraints and a single complicating variable in the objective function. The method is based on finding the distance between the feasible sets of the decomposed problems, and updating the global optimal value according to the value of this distance. The latter is found by exploiting the method of averaged alternating reflections, which is here adapted to the optimisation problem at hand. The method is specially suited for non-linear problems and as our numerical results show, its convergence is independent of the number of variables of each sub-domain. We have tested the method with an illustrative example and with problems that have more than 10,000 variables. Copyright Springer Science+Business Media New York 2015

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  • Nima Rabiei & Jose Muñoz, 2015. "AAR-based decomposition algorithm for non-linear convex optimisation," Computational Optimization and Applications, Springer, vol. 62(3), pages 761-786, December.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:761-786
    DOI: 10.1007/s10589-015-9750-8
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    References listed on IDEAS

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    1. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
    2. Quoc Tran Dinh & Carlo Savorgnan & Moritz Diehl, 2013. "Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 75-111, May.
    3. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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